document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982017>Question 982017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base as shown below.\r<BR>\n" );
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document.write( "Find an equation for the parabola if the vertex is put at the origin of the coordinate system. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602885 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=602885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the equation of the arch be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+ ALIGN=MIDDLE  ALT=\"+h%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the vertical location<BR>\n" );
document.write( "of any point ( x,h ) on the arch.<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the horizontal location <BR>\n" );
document.write( "of any point ( x,h ) on the arch<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "The formula for the x-coordinate of the<BR>\n" );
document.write( "vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the vertex is at the origin,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+0+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+0+ ALIGN=MIDDLE  ALT=\"+b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, now the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+a%2Ax%5E2+%2B+c+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+a%2Ax%5E2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plugging in the point ( 0-,0 ), I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+a%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+0+=+a%2A0+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+0+ ALIGN=MIDDLE  ALT=\"+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+a%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+a%2Ax%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "I am given the points: <BR>\n" );
document.write( "( 14, -22 ) and<BR>\n" );
document.write( "( -14, -22 )<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+a%2A14%5E2+ ALIGN=MIDDLE  ALT=\"+-22+=+a%2A14%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+196a+ ALIGN=MIDDLE  ALT=\"+-22+=+196a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-11%2F98+ ALIGN=MIDDLE  ALT=\"+a+=+-11%2F98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+a%2A%28-14%29%5E2+ ALIGN=MIDDLE  ALT=\"+-22+=+a%2A%28-14%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+196a+ ALIGN=MIDDLE  ALT=\"+-22+=+196a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-11%2F98+ ALIGN=MIDDLE  ALT=\"+a+=+-11%2F98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "The equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+-%2811%2F98%29%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+-%2811%2F98%29%2Ax%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "does it go through ( 14, -22 ) and ( -14, -22 ) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+-%2811%2F98%29%2A14%5E2+ ALIGN=MIDDLE  ALT=\"+-22+=+-%2811%2F98%29%2A14%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+-%2811%2F98%29%2A196+ ALIGN=MIDDLE  ALT=\"+-22+=+-%2811%2F98%29%2A196+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-22+=+-22+ ALIGN=MIDDLE  ALT=\"+-22+=+-22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can check the other point ( -14, -22 )<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-20%2C+20%2C+-26%2C+2%2C+-%2811%2F98%29%2Ax%5E2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+20%2C+-26%2C+2%2C+-%2811%2F98%29%2Ax%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );